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Worked Examples · Example 4
Q.

For the following contingency table of 100 customers classified by sex and whether they liked a product, compute the expected frequency of each cell under the assumption that the two attributes are independent.

LikedDislikedTotal
Male302050
Female203050
Total5050100
Maharashtra MsbshseTextbookSubjectiveImportance★★★★★est
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Step 1 — Note the totals. Row totals: Male =50= 50, Female =50= 50. Column totals: Liked =50= 50, Disliked =50= 50. Grand total N=100N = 100.

Step 2 — Apply Eij=RiCj/NE_{ij} = R_i C_j / N to each cell.

E(Male, Liked)=50×50100=25E(Male, Disliked)=50×50100=25E(\text{Male, Liked}) = \dfrac{50 \times 50}{100} = 25 \qquad E(\text{Male, Disliked}) = \dfrac{50 \times 50}{100} = 25

E(Female, Liked)=50×50100=25E(Female, Disliked)=50×50100=25E(\text{Female, Liked}) = \dfrac{50 \times 50}{100} = 25 \qquad E(\text{Female, Disliked}) = \dfrac{50 \times 50}{100} = 25

Step 3 — Display the expected table.

LikedDislikedTotal
Male252550
Female252550
Total5050100

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